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A212973
Number of triples (w,x,y) with all terms in {0,...,n} and w <= floor((x+y)/3).
4
1, 4, 12, 27, 50, 84, 131, 192, 270, 367, 484, 624, 789, 980, 1200, 1451, 1734, 2052, 2407, 2800, 3234, 3711, 4232, 4800, 5417, 6084, 6804, 7579, 8410, 9300, 10251, 11264, 12342, 13487, 14700, 15984, 17341, 18772, 20280, 21867, 23534
OFFSET
0,2
COMMENTS
For a guide to related sequences, see A212959.
FORMULA
a(n) = 3*a(n-1) - 3*a(n-2) + 2*a(n-3) - 3*a(n-4) + 3*a(n-5) - a(n-6).
G.f.: (1 + x + 3*x^2 + x^3)/((1+x+x^2)*(1-x)^4).
a(n) = (n+1)^3 - A212974(n).
From Ayoub Saber Rguez, Dec 11 2023: (Start)
a(n) = A011379(n+1) - A212972(n).
a(n) = (n^3 + 4*n^2 + 5*n + 2 + (((n+1) mod 3) mod 2))/3. (End)
MATHEMATICA
t = Compile[{{n, _Integer}}, Module[{s = 0},
(Do[If[w <= Floor[(x + y)/3], s = s + 1],
{w, 0, n}, {x, 0, n}, {y, 0, n}]; s)]];
m = Map[t[#] &, Range[0, 60]] (* A212973 *)
LinearRecurrence[{3, -3, 2, -3, 3, -1}, {1, 4, 12, 27, 50, 84}, 50] (* Harvey P. Dale, Jan 24 2015 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Jun 03 2012
STATUS
approved